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Kronecker delta method for testing independence between two vectors in high-dimension.

Ivair R Silva1, Yan Zhuang2, Julio C A da Silva Junior3

  • 1Department of Statistic, Federal University of Ouro Preto, Ouro Preto, MG Brazil.

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Summary
This summary is machine-generated.

This study introduces a new randomized test for Gaussian vector independence in high-dimensional data, addressing limitations of existing methods. The novel approach controls Type I error rates, crucial for accurate statistical inference in complex datasets.

Keywords:
High-dimensional DataKronecker delta covariance structureMultivariate Gaussian VectorsRandomized testing

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Area of Science:

  • Statistics
  • Econometrics
  • High-Dimensional Data Analysis

Background:

  • Conventional independence tests for Gaussian vectors fail in high-dimensional settings (sample size < number of variables).
  • Existing methods cannot reliably control Type I error rates, leading to inaccurate conclusions.
  • There is a critical need for robust statistical tests in high-dimensional scenarios.

Purpose of the Study:

  • To develop a valid statistical test for independence between two Gaussian vectors in high-dimensional data.
  • To overcome the Type I error control limitations of current methodologies.
  • To apply the new test to analyze stock market sector independence during the COVID-19 pandemic.

Main Methods:

  • Development of a novel randomized test utilizing the Kronecker delta covariance matrices estimator.
  • Intensive simulation study to validate the test's performance and Type I error control.
  • Empirical application using stock market data from Brazil.

Main Results:

  • The proposed randomized test effectively controls the Type I error probability at the nominal level.
  • Simulation results demonstrate the superiority of the new method over existing approaches in high-dimensional settings.
  • The test successfully identified patterns of independence between stock returns across different sectors during the COVID-19 pandemic.

Conclusions:

  • The introduced randomized test provides a statistically valid solution for assessing independence in high-dimensional Gaussian vectors.
  • This method offers improved reliability for Type I error control, essential for rigorous statistical analysis.
  • The empirical application highlights the practical utility of the test in financial econometrics, particularly during crisis periods.